Twisted K-theory of differentiable stacks

In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_\alpha \otimes K^j_\beta \to K^{i+j}_{\alpha +\beta}$ are derived. Our approach provides a uniform framework for studying various twisted $K$-theories including the usual twisted $K$-theory of topological spaces, twisted equivariant $K$-theory, and the twisted $K$-theory of orbifolds. We also present a Fredholm picture, and discuss the conditions under which twisted $K$-groups can be expressed by so-called "twisted vector bundles". Our approach is to work on presentations of stacks, namely \emph{groupoids}, and relies heavily on the machinery of $K$-theory ($KK$-theory) of $C^*$-algebras.Comment: 74 page

Structural selective charge transfer in iodine-doped carbon nanotubes

We have investigated iodine intercalated carbon nanostructures by extended X-ray absorption fine structure (EXAFS) and Raman spectroscopies. We discuss here the charge transfer and the iodine–carbon interaction as a function of the carbon nanostructures (graphite, multi-walled, double-walled and single walled nanotubes). The results show that iodine is weakly adsorbed on the surface of all multi-walled nanotubes. By contrast, a charge transfer between iodine and single walled nanotubes is evidenced

PISCO2: the new speckle camera of the Nice 76-cm refractor

We present the new speckle camera PISCO2 made in 2010-2012, for the 76-cm refractor of C\^ote d'Azur Observatory. It is a focal instrument dedicated to the observation of visual binary stars using high angular resolution speckle interferometry techniques to partly overcome the degradation caused by the atmospheric turbulence. Fitted with an EMCCD detector, PISCO2 allows the acquisition of short exposure images that are processed in real time by our specially designed software. Two Risley prisms are used for correcting the atmospheric dispersion. All optical settings are remotely controlled. We have already been able to observe faint, close binary stars with angular separations as small as 0".16, and visual magnitudes of about 16. We also have measured some particularly difficult systems with a magnitude difference between the two components of about 4 magnitudes. This level of performance is very promising for the detection and study of large sets of yet unknown (or partly measured) binaries with close separation and/or large magnitude difference.Comment: 13 pages, 12 figure

Percolation on random networks with arbitrary k-core structure

The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model that generates maximally random networks with arbitrary degree distribution and arbitrary k-core structure. We then solve exactly the bond percolation problem on the HRN model and produce fast and precise analytical estimates for the corresponding real networks. Extensive comparison with selected databases reveals that our approach performs better than existing models, while requiring less input information.Comment: 9 pages, 5 figure

Growing networks of overlapping communities with internal structure

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates. We demonstrate that this simple mechanism gives rise to an effective maximal degree within communities. This observation is related to the anthropological theory known as Dunbar's number, i.e., the empirical observation of a maximal number of ties which an average individual can sustain within its social groups. The second mechanism is based on a recently proposed generalization of preferential attachment to community structure, appropriately called structural preferential attachment (SPA). The combination of these two mechanisms into a single model (SPA+) allows us to reproduce a number of the global statistics of real networks: The distribution of community sizes, of node memberships and of degrees. The SPA+ model also predicts (a) three qualitative regimes for the degree distribution within overlapping communities and (b) strong correlations between the number of communities to which a node belongs and its number of connections within each community. We present empirical evidence that support our findings in real complex networks.Comment: 14 pages, 8 figures, 2 table

Is durum wheat-winter pea intercropping efficient to reduce pests and diseases ?

Intercropping (IC) is known as an agricultural practice which can improve the use of environmental resources (light, nutrients and water) resulting in yield advantages compared to sole cropping (SC) (Willey, 1979) particularly in low input systems. But, diseases ands pests can strongly affect both yield and grain quality in such systems. Now, numerous studies have shown significant reductions in harmful insects and on diseases in IC compared to SC of the same species (Vandermeer, 1989; Kinane and Lyngkjaer, 2002) even if others studies did not confirmed these foundings. The aim of our study was to evaluate the assumption that IC can reduce pea pests (green aphids and weevils), pea ascochyta and main durum wheat diseases (mildew, brown rust, fusarium and septoria)

Complex networks as an emerging property of hierarchical preferential attachment

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.Comment: 12 pages, 7 figure